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Score-based transport modeling for mean-field Fokker-Planck equations

Publication ,  Journal Article
Lu, J; Wu, Y; Xiang, Y
Published in: Journal of Computational Physics
April 15, 2024

We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach. Besides, we provide an error analysis for the algorithm. In numerical experiments, we study three types of mean-field Fokker-Planck equation and their corresponding dynamics of particles in interacting systems. The MSBTM algorithm is numerically validated through qualitative and quantitative comparison between the MSBTM solutions, the results of integrating the associated stochastic differential equation and the analytical solutions if available.

Duke Scholars

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

April 15, 2024

Volume

503

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Lu, J., Wu, Y., & Xiang, Y. (2024). Score-based transport modeling for mean-field Fokker-Planck equations. Journal of Computational Physics, 503. https://doi.org/10.1016/j.jcp.2024.112859
Lu, J., Y. Wu, and Y. Xiang. “Score-based transport modeling for mean-field Fokker-Planck equations.” Journal of Computational Physics 503 (April 15, 2024). https://doi.org/10.1016/j.jcp.2024.112859.
Lu J, Wu Y, Xiang Y. Score-based transport modeling for mean-field Fokker-Planck equations. Journal of Computational Physics. 2024 Apr 15;503.
Lu, J., et al. “Score-based transport modeling for mean-field Fokker-Planck equations.” Journal of Computational Physics, vol. 503, Apr. 2024. Scopus, doi:10.1016/j.jcp.2024.112859.
Lu J, Wu Y, Xiang Y. Score-based transport modeling for mean-field Fokker-Planck equations. Journal of Computational Physics. 2024 Apr 15;503.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

April 15, 2024

Volume

503

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences